Balancing Domain Decomposition by Constraints (BDDC) preconditioners have been shown to provide rapidly convergent preconditioned conjugate gradient methods for solving many of the very ill-conditioned systems of algebraic equations which often arise in finite element approximations of a large variety of problems in continuum mechanics. These algorithms have also been developed successfully for problems arising in isogeometric analysis. In particular, the BDDC deluxe version has proven very successful for problems approximated by Non-Uniform Rational B-Splines (NURBS), even those of high order and regularity. One main purpose of this paper is to extend the theory, previously fully developed only for scalar elliptic problems in the plane, to problems of linear elasticity in three dimensions. Numerical experiments supporting the theory are also reported. Some of these experiments highlight the fact that the development of the theory can help to decrease substantially the dimension of the primal space of the BDDC algorithm, which provides the necessary global component of these preconditioners, while maintaining scalability and good convergence rates.
Pavarino LF, Scacchi S, Widlund OB, Zampini S (2018) Isogeometric BDDC deluxe preconditioners for linear elasticity. Mathematical Models and Methods in Applied Sciences: 1–34. Available: http://dx.doi.org/10.1142/S0218202518500367.
For computer time, this research used also the resources of the Supercomputing Laboratory at King Abdullah University of Science & Technology (KAUST) in Thuwal, Saudi Arabia. The first and second authors’ work was supported by Grants of M.I.U.R. (PRIN 201289A4LX 002) and of Istituto Nazionale di Alta Matematica (INDAM-GNCS). Third author’s work has been supported by the National Science Foundation Grant DMS-1522736.